FORMULA CHAPTER
\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
\mathrm{CI}=\mathrm{A}-\mathrm{P}=\mathrm{P}\left[\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}-1\right]
\mathrm{x}=\mathrm{x}_{0}\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
\mathrm{x}=\mathrm{x}_{0}\left(1-\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
Question: Find the compound amount on ₹10,000 at 10% per year for 2 years.
Calculation: Use A = P(1 + r/100)ⁿ.
Step 1: A = 10000(1 + 10/100)².
Step 2: A = 10000(1.1)² = 12100.
Answer: The compound amount is ₹12,100.
\mathrm{CI}=\mathrm{A}-\mathrm{P}=\mathrm{P}\left[\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}-1\right]
Question: Find the compound interest on ₹10,000 at 10% per year for 2 years.
Calculation: Use CI = P[(1 + r/100)ⁿ − 1].
Step 1: CI = 10000[(1.1)² − 1].
Step 2: CI = 10000(1.21 − 1) = 2100.
Answer: The compound interest is ₹2,100.
\mathrm{x}=\mathrm{x}_{0}\left(1+\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
Question: A population of 2,000 grows by 5% per year. Find it after 2 years.
Calculation: Use x = x₀(1 + r/100)ⁿ.
Step 1: x = 2000(1.05)².
Step 2: x = 2000 × 1.1025 = 2205.
Answer: The population after 2 years is 2,205.
\mathrm{x}=\mathrm{x}_{0}\left(1-\frac{\mathrm{r}}{100}\right)^{\mathrm{n}}
Question: An asset worth ₹20,000 depreciates by 10% per year. Find its value after 2 years.
Calculation: Use x = x₀(1 − r/100)ⁿ.
Step 1: x = 20000(0.9)².
Step 2: x = 20000 × 0.81 = 16200.
Answer: The depreciated value is ₹16,200.
